A novel method based on constellation structure is proposed to identify PSK and QAM modulation of different orders, in the slow and flat fading channel. The proposed method does not require training for threshold optimization and considers carrier frequency, symbol rate, and phase offset unknown. The symbol rate is estimated using the spectrum of the instantaneous phase of the complex baseband signal. Carrier frequency offset (CFO) is estimated and corrected from the downconverted signal and downsampled to the estimated symbol rate for extraction of constellation points. The phase offset is determined based on the symmetrical structure of constellation. The features extracted using k-medoids are used for classification of the final modulation scheme. Results show that the proposed algorithm outperforms some existing classifiers and offers lower computational complexity compared to algorithms based on subtractive clustering. © 1997-2012 IEEE.